Piezoelectric quartz element



March 15, 1938. v A, B KOV Y 2,111,383

I EEEEEEEEE TRIO UART EEEEEE NT Filed Sept. 30, 1935 2 Sheets-Sheet l March 15, 1938. s. A. BOKOVOY PIEZGELECTRIC QUARTZ ELEMENT Filed Sept. 30, 1935 2 Sheets-Sheet 2 no: lull:

WHO: \SOQ Patented Mar. 15, 1938 2,111

S AT E N PIEZOELEWFtIC ELEMENT Samuel A. iiokovoy, Audubon, N. 3., assignor to Radio Corporation of America, a corporation oi. Delaware Application September 343 i935, Serial No. 12,915

3.3 Glaziers {6H, iii-$2?) This invention relates to the piezo-electric art tion of the arrow in Fig. 2 showing the position and particularly to the cutting of quartz piezo= ot a number of blanks out from the bar of Fig. 2.

rricc electric elements. Fig. 4 shows the right hand blank of Fig. 3 re- An object or" the invention is to provide a quartz moved. 5 piezo-electric element possessing a unitary free" Fig. 5 shows the left hand blank of Fig. 3 re- 5 dom for its X-axis mode of vibration. r moved, the plane of projection being perpenclic Another object of the invention is to provide a ular to the plane of the paper. process for cutting a quartz crystal to procure a "Fig. 6 is a cross sectional view taken on the line piezo-electric element that will oscillate efficiently SF-Y of Fig. 1 showing the rotation of the at but one of several X or contour-mode freblanks about an Y-axis of a mother crystal and lil quencies originally present. with respect to the major and minor apex faces. Another object of the invention is to provide a Figs. '7, 8 and 9 are, respectively, families of crystal of the type described which, when vicurves, empirically obtained, each showing the brated at its single contour-mode frequency will single frequency region, the corresponding ireexhibit a substantially zero temperature coeniquency constant and characteristic temperature 15 cient of frequency. coefiicient for a variable length-wide ratio for the Another object of the invention is to provide a low, normal and upper modes of frequency re quartz piezo-electric element free to oscillate at spouse along the X-axis. only two fundamental frequencies, one of the fre- The present invention contemplates and its quencies bearing a multiple or other desired relapractice provides a piezo-electric element having 20 tionship to the other, the lower frequency being all, or if desired, less than all, of the following a function of the X-axis dimension of the element operating characteristicsand the higher frequency being a function of its (a) A zero temperature coefficient of frequency thickness dimension. Y or a temperature coeficient of either sign and of Another object of the invention is to provide a a desired low value. 25 crystal of the type described which, when vi- This desired operating characteristic obtains,

brated at its higher (1. e. its tlficlrness-mode) frein accordance with the present invention, by reaquency will exhibit a temperature coeilicient of, son of a predetermined orientation of the prin- 1 frequency no greater than substantially minus cipal surfaces of the element with respect to the 15 cycles per million per degree centigrade. plane of a minor, or conversely, a. major apex 0 Another object of the invention is to provide a face of the mother crystal from which the elesimple, accurate and efiicient mode of procedure ment is cut. in the cutting of quartz crystals to eliminate as (h) A unitary freedom for its X-axis mode of far as possible any uncertainties with regard to vibration. The significance of this feature of the the oscillatory characteristics of the finished invention will perhaps be best understood when 35 piezo-electric elements. it is recalled that with known piezo-electric ele- Other objects and advantages will be apparen ments several modes of vibration and conseand the invention will be best understood by quently several frequencies (which may bewithin reference to the following specification and to 50 is. c. or so of each other) are possible of the accompanying drawings wherein:. achievement even when the crystal is employed Fig. 1 is a plan view of a natural or mother in a non-regenerative circuit. Another mode of quartz crystal, the optic (Z) axis of which is vibration, namely the thickness-mode is present perpendicular to the plane of projection; the rela in any case but because, in a given crystal, the tive location of the major and minor faces, the frequency characteristic of this mode is so much apex, the electric (X) axes and the mechanical higher than that of any of the X-mode frequen- 45 (Y) axes being here illustrated as an aid to a clear cies, it is not disturbing.

understanding of the system of orientation fol= The single frequency which is a function of lowed in producing piezo-electrlc elements within that one of the greater dimensions of the element the present invention. which coincides with an electric (X) axis of the Fig. 2 shows in outline and in perspective a mother crystal obtains, in accordance with the 50 piece of natural quartz having a section cut and invention by reason of a predetermined length divided to provide a rough bar having top and width ratio. As will hereinafter more fully ap bottom surfaces lying in planes which are normal pear this frequency may be characteristic of any to the optic (Z) axis. of the natural modes of vibration but is prefer- Fig. 8 an elevatiollal V ew oo ng in the oirecably characteristic of one of the stronger modes,

i. e. the upper" "normal or "low X-modes of vibration. The length-width ratio is given for each mode.

(0) A crystal may be so cut in accordance with the present invention that the second or thickness-mode" frequency, which is always present, will bear a predetermined useful relation to the single X-mode frequency previously mentioned.

Thus it is practical to so cut a quartz crystal that the finished element will oscillate at a frequency of, say k. c. and also at 1000 k. 0., 200 k. c. and 2000 k. c., or at any two other desired widely separated frequencies. This characteristic is achieved by correlating the length, the width and the thickness of the element in accordance with a given formula. v

Since the present invention involves a system of orientation in which the major and/or minor apex faces of the mother crystal are employed as reference planes it is first necessary to locate and identify these faces. .As all unbroken quartz crystals are uniformly shaped hexagonal bi-pyramids this is a relatively simple step.

Referring to Figs. 1 and 2 of the drawings it will be seen that certain of the terminal faces of the quartz extend to the apex of the pyramid. These faces are designated M and are the major apex faces. Those terminal faces which do not touch the apex are designated N and are the minor apex faces of the crystal. Occasionally a mother crystal will be found in which more than three of the cap or apex surfaces extend to the tip of the pyramid, other crystals may have their pyramid ends broken off. No confusion, however, need exist as to the virtual location of the major and minor-apex faces of a broken or otherwise abnormal crystal providing that the side faces "m" or "n, or one of them, is intact for it will be apparent from an inspection of Fig. 2 that those side edges of the mother crystal which approach each other in the direction of its ends terminate in a major apex face, while those which diverge in this direction terminate in a minor apex face. This is so in the case of both "lefthand" and right-hand" quartz. Fig. 1 is further marked to show the electric (X) axes and mechanical or crystallographic (Y) axes of the mother crystal. The optic (Z) axis, marked in Fig. 2, is perpendicular to the plane of pro- Jection in Fig. 1.

If the element is so cut in accordance with the invention that its principal surfaces (1. e. top and bottom) fall in planes which are substantially parallel to an X (electric) axis and inclined at an angle of between 37-40, say 385, toward parallelism with the plane of a minor apex face, or at an angle of between 5355, say 54 towards parallelism with a major apex face, it will possess a zero or some other low temperature coeflicient of frequency.

The preliminary steps in the cutting of a crystal may proceed in the manner usual in the cutting of a standard Y-cut blank. Thus referring to Fig. 2, a section 2, say one inch thick, should first be sliced from the body of the crystal and a bar 3 in turn cut from the section. As indicated in Fig. 3 the thickness dimension of this bar 3 is parallel to the Z (optic) axis, the width is parallel to an X (electric) axis and the length is parallel to a Y (mechanical) axis.

The blanks 4 and I, from which the finished elements of the present invention are formed, are then sliced from this bar at an angle within the indicated range. As previously set forth and as indicated in Fig. 6, the 37-40 low temperature coemcient tilt is in a direction from the Z axis toward parallelism with a minor apex face and that of the 53-55 low temperature coeilicient tilt is in a direction toward parallelism with a major apex face.

In the interest of clearness and brevity that dimension of the blanks, and of the finished elements which lie in a plane tilted from parallelism with the Z-axis will hereinafter be referred to in the drawings and in the specification as the Z+6 dimension. The other of the two greater dimensions of the element is parallel to an X-axis and is designated the X-axis dimension. The thickness dimension lies in a plane which intersects a Y-axis and is occasionally referred to as the Y+0 dimension.

When the blanks 4 and 5 of the correspondingly numbered figures are correctly proportioned as to width and length and are properly finished it will be found that they possess a zero or some low temperature coefficient of frequency and further, will, unless strongly excited, respond to but a single X-mode of vibration.

Regardless of which of the two described blanks is selected for finishing, the dimension of the finished element should first be determined in accordance with the formula where j is the desired single frequency in megacycles.

K is a constant which is the same for all frequencies characteristic of a given mode but differs for each of the available modes.

X is the dimension of the element along the X-axis expressed in mils of an inch.

Example ,1

Given a blank cut with its principal surfaces tilted at an angle of substantially 385 towards parallelism with the plane of a minor apex face (blank 5 of Figs. 3, 5 and 6) and assuming that a finished element possessing the following operating characteristics is required:

(a) zero temperature coefficient of frequency (b) say, 100 k. c.

(c) a second frequency response of, say, 10 times that of the 100 k. 0. frequency.

Assuming further, for purposes of illustration, that the 100 k. 0. frequency to be achieved is to be a low-mode frequency.

Referring then to Fig. 7 of the drawings and particularly to curve A it will be seen that the dimension of the element along its X-axis dimension expressed in mils of an inch should be equal to the desired low-mode frequency (100 k. c.) expressed in megacycles divided into any .constant (K) between substantially 218 and 2'75 and that the other of the two greater dimensions of the crystal (1. e. the Z+e dimension Fig. 5) should be n i lly .36 to .55 times that of the x-axis dimension, depending upon the x -axis constant selected.

It will be noted, however, by reference to curve B of this Fig. 7 that a random selection of a constant within the 218-275 K single frequency range will not ensure a finished element having an exactly zero temperature coefdcient of frequency when the Z+9 dimension, as in the example given, is tilted precisely 38.6 towards parallelism with a minor apex face of the mother crystal. For this angle of orientation the zero temperature coemci nt is achieved when the cona single X-mode frequency. response of,

stant (K) selected is substantially 242.1 and the ratio of the Z+9 dimension to that of the X-axls dimension is substantially .463.

Applying Formula 1 it will be seen that the dimensions of a piezo-electric element filling requirements a and b will be 242.1 .1 'thus, the Ii -axis dimension will be 2421 mils of an inch.

The 2+9 dimension will be 2421 mils times .463 (the ratio) or substantially 1,120.9 mils of an inch.

The formula required to achieve the third (c) desired characteristic i. e. a thickness or Y+6 mode frequency response of 1000 k. c., is

where d is the dimension along the Y+9 axis, f is the Y+6 mode frequency expressed in megaeycles and K is equal to substantially 67.

As the second frequency required in this instance is 1000 k. c. it is apparent that the element should be ground or lapped to a thickness of substantially 67 mils of an inch.

Example 2 Referring to curve A of Fig. 8 it will be seen that the single frequency range of constants K for the normal X-mode of vibration is substantially 109-433 and the dimensional ratio is 3-1.3. The preferred constant K is 120 and the preferred Curve A of Fig. 9 shows clearly that the range of constants K for an element cut to respond to a single upper mode frequency is substantially 97-118 and the length-width ratio between 2 and 3. For the 38.6 zero temperature tilt the preferred constant K is 107.5 and the dimensional ratio is 2.5. Accordingly, the dimension along the X-axis for 100 k. c. response will be 1075 mils of an inch and the Z+9 dimension 2687.5 mils of .an inch. The thickness of the element for the Y+6 1000 k. 0. response, as in the two prior examples, should be 67 mils of an inch;

The formula for the single frequency X-mode of response holds true for all frequencies between substantially 20 k. c. and 750 k. c. The thickness or Y+6 frequency range is substantially 400 k. c.

to, say, 10 megacycles depending to some extent upon practical limits of lapping thin plates.

The curves of Figs, 7, 8 and 9 are for the 37-l0 tilt about the X-axis toward parallelism with a minor apex face. The constants therein disclosed do not hold good for the 53-55 blank.

All of the examples set forth are fora 38.6 angle of rotation, the permissible range of angles, however, is that stated, i. e. 37-40. If, whether through accident or design, the element is given a tilt other than 385 and within this range it will not exhibit an exactly zero temperature coefficient of frequency, however this desired operating characteristic may be achieved for a specific angle by altering the ratio in a direction corresponding to the direction of departure from 38.6. That is to say assuming a blank to be cut at 39.5", the

ratio should be slightly increased to retain the zero temperature coefficient. The curves B of Figs. 7, El and 9 are intended primarily to indicate the direction of frequency drift (that is in a positive or negative direction) with respect to the effects of temperature change rather than the amount of change per degree of temperature. The exact shift per degree C will be found to vary with the frequency for which the element is cut. A 'crystal cut in accordance with the present invention to oscillate at a single X-mode frequency and at a desired Y+9 mode frequency will ordinarily exhibit an exactly zero temperature coefficient only while operating at its X-mode frequency, the temperature coefficient of frequency of the element while vibrating at its Y+9 frequency will, however, be quite low, usually within +15 cycles per million per degree C.

Although certain specific ways and means for accomplishing the object of the invention have been set forth it will be understood that they have been given by way of example and should not be construed as limitations to the scope of the invention. Neither is it to be understood that any statements herein made in regard to the values or relationships between dimensions and frequency are other than close approximations. It is well known in the art that in order to obtain the frequency characteristics of a piezo-electric plate with the precision that is required frequent tests of frequency characteristics should be made between successive stages of the grinding operation. The invention, therefore, is not to be limited except insofar as is necessitated by the prior art and by the spirit of the appended claims.

What is claimed is:

1. A quartzpiezo-electric element cut from a mother "crystal having major and minor apex faces, said element having its principal surfaces in planes which are substantially parallel to an X-axis and inclined at an angle of substantially 37 to 40 from the Z-axis toward parallelism with the plane of a minor apex face, the dimension of each of said surfaces along the X-axis expressed in mils of an inch being equal to where f is a frequency of the element expressed in megacycles and K is equal to 218 to 275, and the other dimension of said surfaces, similarly expressed, is equal to substantially .55 to .36 times said first mentioned dimension, said element being characterized by exhibiting a substantially unitary freedom for its X-axis mode of vibration and a low temperature coefficient of frequency.

2. The invention as set forth in claim 1 further characterized in that the thickness of said element expressed in mils of an inch is equal to where ,f is a second frequency of said element expressed in megacycles and K is equal'to sub,- stantially 67.

3. A quartz piezo-electric element cut from a mother crystal having major and minor apex faces, said element having its principal surfaces in planes which are substantially parallel to an X-axis and inclined at an angle of substantially 38.6 from the Z'-axis toward parallelism with the plane of a minor apex face, the dimension of each of said surfaces along the X-axis expressed in mils of an inch being equal to in which I is a frequency of the element expressed in megacycles and K is equal to 242.1 and the other dimension of said surfaces, similarly expressed, is equal to substantially ,463 times said first mentioned dimension, said'element being characterized by exhibiting a substantially unitary freedom for its X-axis mode of vibration and a substantially zero temperature coefficient of frequency.

4. The invention set forth in claim 3 further characterized in that the thickness of said element expressed in mils of an inch is equal to where ,f is a second frequency of said element expressed in megacycles and K is equal to substantially 67.

5. A quartz piezo electric element cut from a mother crystal having major and minor apex faces, said element having its principal surfaces in planes which are substantially parallel to an pressed in mils of an inch being equal to where f is a frequency of the element expressed in megacycles and K is equal to 109 to 133, and the other dimension of said surfaces, similarly expressed, is equal to substantially 1.3 to .8 times said first mentioned dimension, said element being characterized by exhibiting a substantially unitary freedom for its X-axis mode of vibration and a low temperature coefficient of frequency.

6. The invention as set forth in claim 5 further characterized in that the thickness of said element expressed in mils of an inch is equal to where f is a second frequency of saidelement expressed in megacycles and K is equal to substantially 67. v

7. A quartz piezo-electric element cut from a mother crystal having major and minor apex faces, said element having its principal surfaces in planes which are substantially parallel to an X-axis and inclined at an angle of substantially 38.6 from the Z-axis toward parallelism with the plane of a minor apex face, the dimension of each of said surfaces along the X-axis expressed in mils of an inch being equal to in which f is a frequency of the element expressed in megacycles and K is equal to 120, and the other dimension of said surfaces, similarly expressed, is equal to substantially 1.02 times said first mentioned dimension, said element being characterized by exhibiting a substantially unitary freedom for its X-axis mode of vibration and a substantially zero temperature coefficient of frequency.

8. The invention as set forth in claim 7 further characterized in that the thickness of said element expressed in mils of an inch is equal to where j is a second frequency of said element expressed in megacycles and K is equal to substantially 67.

9. A quartz piezo-electric element cut from a mother crystal having major and minor apex faces, said element having'its principal surfaces in planes which are substantially parallel to an X-axis and inclined at an angle of substantially 37 to 40 from the Z-axis toward parallelism with the plane of a minor apex face, the dimension of each of said surfaces along the X-axis expressed in mils of an inch being equal to where f is a frequency of the element expressed in megacycles and K is equal to 97 to 118, and the other dimension of said surfaces, similarly expressed, is equal to substantially 3 to 2 times said first mentioned dimension, said element being characterized by exhibiting a substantially unitary freedom for its X-axis mode of vibration and a low temperature coefficient of frequency.

10. The invention as set forth in claim 9 further characterized in that the thickness of said element expressed in mils of an inch is equal to where f is a second frequency of said element expressed in megacycles and K is equal to substantially 6'7.

11. A quartz piezo-electric element cut from a mother crystal having major and minor apex faces, said element having its principal surfaces in planes which are substantially parallel to an X-axis and inclined at an angle of substantially 38.6" from the Z-axis toward parallelism with the plane of a minor apex face, the dimension of each of said surfaces along the X-axis expressed in mils of an inch being equal to in which I is a frequency of the element expressed in megacycles and K is equal to 107.5, and the other dimension of said surfaces, similarly expressed, being equal to substantially 2.5 times said first mentioned dimension, said element being characterized by exhibiting a' substantially unitary freedom forits x-axis mode of vibration andasubstantially zero temperature coeflicient of surfaces, said element having its principal sur- Irequency. faces in planes which are substantially parallel 12. The invention as set forth in claim 11 furto an X-axis and inclined at an angle of from ther characterized in that the thickness of said substantially 37 to substantially 40 with re- 5 element expressed in mils of an inch is equal to spect to the Z-axis in a direction towards par- 5 allelism with the plane of a minor apex surface, 7 said element having its length and width relatively so proportioned with respect to the angle where f is a second frequency of said element formed by the intersection of said surfaces with 10 expressed in megacycles and K is equal to subsaid Z-axis that it possesses a unitary freedom for 10 stantially 67. it's X-axis mode of vibration.

13. A quartz piezo-electric element cut from .a mother crystal having major and minor apex SAMUEL A. BOKOVOY. 

